In this paper we study certain \(p\) -adic properties of the Stirling numbers of the second kind \(S(n,k)\)  and of the first kind
\(s(n,k)\) .
In recent years several papers appeared in which the \(p\) -adic properties of these numbers and the 2-adic properties, in particular have been investigated.
Various efforts were made to determine congruences and the \(p\) -adic valuations of both kinds of Stirling numbers, e.g., [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, and [16]}, [17]}, [18]}, [19]}, [20]}, etc.
Some of these results are universal and deal with \(\nu _p(S(n,k))\)  and \(\nu _p(s(n,k))\)  with no particular restrictions on \(n\)  and \(k\)  while other results focus on cases when \(n\)  is in the form of \(c p^h\)  with \(c,h\in \mathbb {Z}^+\) . There are result of an experimental nature too, e.g., Amdeberhan et al. [3]} establish patterns in the 2-adic evaluation of \(S(n,k)\)  with different values of \(k\) .
